J Therm Anal Calorim DOI 10.1007/s10973-017-6615-7 Thermal oxidation reaction of paraffin with O2 and N2O under different pressures Lin-lin Liu1 • Song-qi Hu1 • Pei-jin Liu1 • Guo-qiang He1 • Guan-feng Wu1 Received: 8 January 2017 / Accepted: 26 July 2017 Ó Akadémiai Kiadó, Budapest, Hungary 2017 Abstract Thermal reaction of paraffin with oxidizers could provide valuable information concerning the regression rate and combustion efficiency of paraffin-based fuels. In this paper, thermogravimetric–differential scanning calorimetry experiments were carried out for paraffin under O2 and N2O atmosphere, and the thermal reaction kinetics of paraffin under different pressures of O2 and N2O was estimated through the non-isothermal measurements and model-free isoconversional methods. The results show that the oxidation of paraffin under O2 and N2O atmosphere represents the multistage reaction process; the obtained activation energy (Ea) is much close by using different model-free isoconversional methods, and paraffin is easier to be oxidized under O2 because of the lower Ea and lower reaction temperature; Pressure plays a positive effect on the oxidation of paraffin, especially under O2 atmosphere. Keywords Paraffin Kinetic parameters Thermal oxidation reaction Hybrid motor fuel Introduction Hybrid motor offers several important advantages over the liquid and solid rockets mainly due to the storage of solid fuel and liquid oxidizer in separate phases, such as safety, reliability, throttling of thrust, shutdown–restart ability, environmental friendliness, low cost . Normally, the high molecular weight hydrocarbons, such as hydroxylterminated polybutadiene (HTPB) , polymethyl methacrylate (PMMA)  and polythene (PE) , are used as the fuels of hybrid motor; however, the low regression rate of these fuels is the most key issue for the development and application of hybrid motor . Liquid tiny droplets with low surface tension and low viscosity are produced at the tips of the waves during the combustion of paraffin-based fuels which results in a regression rate 3–4 times higher than HTPB [6–8]. Therefore, paraffin-based fuels are generally regarded as the most promising fuels of hybrid motor. Nowadays there are many researches about the paraffin-based fuels mainly in the fields of regression rate, combustion efficiency, combustion instability and mechanical behavior [9–11]. Ignition and combustion mechanisms are important issues because they can provide valuable information concerning regression rate and the combustion efficiency of fuels. Considering that O2 and N2O are the mostly used oxidizers in hybrid motor and paraffin is the most important constituent of paraffin-based fuels, TG and DSC experiments were carried out for paraffin under O2 and N2O atmosphere in this study. And then, the thermal reaction kinetics of paraffin under different pressures of O2 and N2O were estimated through the non-isothermal measurements and model-free isoconversional methods. Experimental & Lin-lin Liu firstname.lastname@example.org 1 Science and Technology on Combustion, Internal Flow and Thermal-Structure Laboratory, Northwestern Polytechnical University, Xi’an 710072, People’s Republic of China Semi-refined paraffin with a melting point having a range of 60–80 °C was purchased from Daqing Petrochemical Company, China Petroleum Corporation, and the main composition is C22H46 1.9%, C23H48 6.4%, C24H50 12.4%, C25H52 16.3%, C26H54 16.9%, C27H56 14.8%, C28H58 123 L. Liu et al. 11.9%, C29H60 8.8%, C30H62 4.8%, C31H64 2.9%, C32H66 1.6%, C33H68 0.5%. Simultaneous TG–DSC (METTLER TOLEDO TG/DSC 1) and high-pressure DSC (METTLER TOLEDO DSC 827e) were used to investigate the thermal reaction process of paraffin with O2 and N2O under atmospheric pressure, 1, 2 and 4 MPa. Samples weighing about 3 mg were heated from 30 to 700 °C with a heating rate of 10, 20, 30 and 40 °C min-1, respectively, and the flow rate of the sweeping gas is set as 30 mL min-1. In order to obtain some information concerning the decomposition process of paraffin, simultaneous TG–DSC experiment under argon atmosphere was also carried out in this study. Results and discussions Thermal decomposition of paraffin TG/DSC experimental results of paraffin at argon atmosphere with 10 °C min-1 heating rate are shown in Fig. 1. Figure 1 shows that there was an obvious endothermic peak with peak temperature located at 70.5 °C, and this was resulting from the melt of solid paraffin. The mass of the sample started decrease when the temperature reached about 210 °C with negligible endothermic effect. The mass loss speeded up at about 241 °C, and the mass loss stopped at 354 °C with mass loss of 99.7%. In addition, the mass loss was accompanied with the weak endothermic process. Paraffin consists mainly of alkane which is easily to decompose with the products of shorter-chain-length paraffin and olefin under higher temperature, and the produced shorter-chain-length paraffin will decompose again . The products with lower molecular weight could escape from the sample which would result in the mass loss. Meanwhile, the decomposition of paraffin needs energy, so there was a weak endothermic decomposition peak in DSC curve. Thermal reaction of paraffin with O2 and N2O Paraffin-based fuels react with oxidizer in hybrid motor, and Fig. 2 shows the TG and DSC curves of paraffin at O2 and N2O atmosphere with 10 °C min-1 heating rate. It can be seen from Fig. 2 that the mass loss started at 178 °C under both atmosphere which is lower than the thermal decomposition temperature (210 °C) of paraffin shown in Fig. 1. This means that the gaseous oxidizer could react with liquid paraffin directly at lower temperature and produced small amount of gaseous products. The mass loss speeded up at 205 °C under N2O atmosphere and at 220 °C under O2 atmosphere, respectively, and the samples lost most of their mass during the reactions which was similar to the cases shown in Fig. 1. The DSC curves show that the oxidation reaction of paraffin with O2 could release much more heat than the case with N2O, which agrees with the thermodynamic calculation results. There were weak exothermic peaks located at 484.5 and 506.5 °C under O2 and N2O atmosphere, respectively, which was caused by the oxidation of carbon decomposed by paraffin. In addition, the DSC curves represented insignificants bimodal which may suggest the multistage of the reactions. Oxidizers reacted with liquid paraffin directly at lower temperature, and the reaction was much mild due to the low reaction rate of heterogeneous reactions and the low temperature. Gaseous hydrocarbon products were produced from the decomposition of paraffin, and these products would be oxidized by oxidizers which will improve the decomposition of paraffin. Meanwhile, the high temperature also favors the reactions of liquid paraffin and oxidizer. Therefore, the reactions of paraffin and oxidizer appeared the multistage reactions . 20 8 80 2 40 0 20 0.33% 70.5 °C 354 °C 0 100 200 300 –2 400 500 600 700 Temperature/°C Fig. 1 TG and DSC curves of paraffin at argon atmosphere 123 Exo N2O 10 Mass/% 60 Heat flow/W g–1 Endo 4 15 O2 178 °C 60 270 °C 40 5 484.5 °C 20 0 506.2 °C 70.5 °C 2.02% 0 –5 1.37% 100 200 300 400 500 600 Heat flow/W g–1 Endo 6 Exo 210 °C 80 Mass/% 255 °C 100 100 700 Temperature/°C Fig. 2 TG and DSC curves of paraffin at O2 and N2O atmosphere Thermal oxidation reaction of paraffin with O2 and N2O under different pressures Considering that the first exothermic peak was much obscure and little reliable information could be obtained even after the peak fit procedure, single peak was regarded when the DSC data were used to get the thermal reaction kinetics parameters. Thermal reaction kinetics The reaction rate of condensed phase chemical reactions usually depends on the temperature T and the reactant conversion percentage a, and is expressed by  ð1Þ The function f(a) is the kinetic model which may take a large number of mathematical forms depending on the physical mechanism. For the non-isothermal kinetic analysis, k(T) which represents the temperature dependence of the rate constant is commonly described with the following Arrhenius equation: E kðTÞ ¼ A exp ð2Þ RT where A is the pre-exponential factor, E is the activation energy, and R is the gas constant. For non-isothermal experiments which are carried out with linear heating rates b = dT/dt, the reaction rate is expressed as da A E ¼ exp f ðaÞ ð3Þ dT b RT The kinetic analysis based on model-free methods allows the apparent activation energy to be evaluated for different constant extents of conversion without assuming any particular form of the reaction model. In this study, model-free isoconversional Flynn–Wall–Ozawa (FWO) method [15, 16], Kissinger–Akahira–Sunose (KAS) method [17, 18] and Starink method  were used to evaluate the apparent activation energy Ea of the reactions. The three methods could be expressed by Eqs. 4–6. Heating rate/ °C min-1 Peak temperature/°C O2 atmosphere N2O atmosphere 1/ atm 1/ MPa 4/ MPa 1/ atm 1/ MPa 4/ MPa 10 250 239 230 271 262 257 20 260 249 241 279 270 266 30 266 256 247 284 275 271 40 271 260 251 287 279 275 The fitted straight lines with Y (Y was set as lg b, lnb/ T1.8 and lnb/T1.8 when FWO, KAS and Starink methods were used) as vertical axis and with 1/T as horizontal axis are shown in Fig. 3. The fitting report suggests that the correlation coefficients of the slope were all more than 0.99, which indicates the high reliability of DSC data and model-free isoconversional methods used in this study. Table 2 represents the Ea obtained by the methods mentioned above. Table 2 shows that the Ea obtained from different methods is much close under the same atmosphere which indicates the isoconversional-method-free characteristics of the reactions to a large degree, so the average value could be used in the analysis. Table 2 also suggests that the Ea is much lower under O2 atmosphere which means paraffin is easier to react with O2, and this result corresponds to the lower reaction temperature of them. In addition, Ea decreases from 149 to 136 kJ mol-1 when the pressure increases from 1 atm to 4 MPa under O2 atmosphere, and Ea decreases from 208 to 178 kJ mol-1 for the cases under N2O atmosphere. And then, pressure 2.0 FWO-O2-1 atm FWO-O2-1 MPa FWO-O2-4 MPa FWO-N2O-1 atm FWO-N2O-1 MPa FWO-N2O-4 MPa 1.5 AEa Ea 2:315 0:4567 lg b ¼ lg RgðaÞ RT ð4Þ b AR Ea ln 2 ¼ ln T Ea gðaÞ RT ð5Þ b Ea þ constant ln 1:8 ¼ 1:0037 T RT ð6Þ 1.0 Y da ¼ kðTÞ f ðaÞ dT Table 1 Peak temperature information of the reactions –8 According to Eqs. 4–6, plotting lg b, lnb/T2 and lnb/T1.8 against 1/T, respectively, should give straight lines, and apparent activation energy Ea is proportional to the activation energy the slope of lines. Table 1 shows the peak temperature Tp of DSC curves for the thermal reaction of paraffin under different atmosphere and pressure, which was used to obtain Ea. –10 1.80 1.85 1.90 1.95 2.00 1000/T/K–1 Fig. 3 The fitted curves: the solid symbols represented the data obtained by using FWO method, and the hollow and cross-insidehollow symbols represented the ones by using KAS and Starink methods under the corresponding conditions 123 L. Liu et al. Table 2 The fitted Ea of thermal reactions Method Activation energy Ea/kJ mol O2 atmosphere -1 N2O atmosphere 1/atm 1/MPa 4/MPa 1/atm 1/MPa 4/MPa FWO 150 141 137 207 191 178 KAS 148 139 135 208 192 178 Starink 149 140 136 209 193 178 plays a positive effect on the oxidation of paraffin, especially under O2 atmosphere. Conclusions (1) (2) (3) Almost all the paraffin sample could be decomposed into gaseous products at the temperature range of 210–354 °C, but the oxidation of paraffin starts at 205 and 220 °C under O2 and N2O atmosphere, respectively, which indicates the multistage of the oxidation reaction process. The results of apparent activation energy Ea are much close by using different model-free isoconversional methods, and paraffin is easier to react with O2 because of the lower Ea and lower reaction temperature. Ea decreases with pressure indicating pressure plays a positive effect on the oxidation of paraffin, and this effect is more obvious under O2 atmosphere. 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